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Re: st: "Proper" usage: Univariate, bivariate, multivariate, multivariable

From   Nick Cox <>
To   "" <>
Subject   Re: st: "Proper" usage: Univariate, bivariate, multivariate, multivariable
Date   Tue, 15 Oct 2013 21:25:10 +0100

Flattered to be quoted, but for once I will try just to comment rather
than make assertions about "proper" usage. I will fail, but here goes:

0. Outcome is a good term anyone can borrow, but response, criterion
variable, etc. are common in many fields and "dependent variable"
refuses to lie down and die quietly. Exposure variable I don't think
is a term much encountered outside epidemiology or biostatistics, not
that makes it wrong: it is good, evocative terminology when it fits!
The number of synonyms for what many people just call "right-hand side
variables" is too large to fit in a small space.

1. It is my impression that "multivariable" is mostly biostatistical
in usage. I have not ever heard that it meant something other than
"multivariate" but am happy to be corrected. If there is a
distinction, it sounds too fine to be remembered, just as the
difference between "homogenous" and "homogeneous" is too subtle to be

2. Univariate, bivariate, multivariate just count the number of
variables, one, two or many. (Somewhere long ago I read about a not
very numerate tribe, whose number system supposedly gave out after
two, so that their number words were equivalent to "one", "two" or
"many". Nowadays I tend to wonder whether it was the anthropologists
who were misreading what they were told.)

3. Statistical science spans people who are happy to talk about a
model for one variable ("normal distribution model") and people who
won't entertain the word "model" unless there are variables being

4. Oddly, "multivariate" has morphed over say 50 years from meaning "I
have many variables" to meaning "I have many response variables, or
variables all on the same footing". A quick test is whether you regard
multiple regression as a multivariate method (I say no). However, I
don't buy the idea that "univariate" and "bivariate" strictly refer to
how many response variables you have in a model. I don't think that
matches usage.


On 15 October 2013 20:51, Nicole Boyle <> wrote:
> Hello all,
> There are some terms commonly used in the literature that seem (to me)
> technically misused. Nick Cox addressed a similar question
> previously*, but I'm unfortunately still confused as to the proper
> usage of these terms.
> My understanding:
> (1) Multivariable: Model with more than one exposure var and one outcome var.
> (2) Multivariate: Model with one or more exposure vars and multiple
> outcome vars.
> (3) Multivariable model != Multivariate model
> (4) Univariate: Not a true model, but just looks at distribution of
> one "exposure" var within a group. This method may be repeated across
> multiple groups, e.g. demographics table with no test statistics. (In
> my humble opinion, this should be instead termed "univariable" to
> indicate a single variable, since "univariate" seems to imply a model
> with one outcome variable and an undefined number of exposure vars.)
> (5) Bivariate: Model with one exposure var and one outcome var. (In my
> very novice opinion, this should instead be termed "bivariable" to
> indicate two variables, since "bivariate" seems to imply two outcome
> variables with an undefined number of exposure vars.)
> (6) Univariate!=Bivariate
> I've decided to run this by you all while writing what feels like a
> strange sentence: "Univariate and multivariable Cox proportional
> hazards models..." Perhaps this should be "Bivariate and
> multivariable" or even "Bivariable and multivariable"?
> What would be considered proper usage (where "proper usage" might be
> defined as technically correct, or might even be defined as
> technically incorrect but widely accepted)?
> Thanks so much for your consideration,
> Nicole Boyle
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